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課程名稱 |
微積分3
CALCULUS (3) |
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開課學期 |
113-2 |
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授課對象 |
化學工程學系 |
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授課教師 |
蔡國榮 |
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課號 |
MATH4008 |
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課程識別碼 |
201E49830 |
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班次 |
07 |
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學分 |
2.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
第1,2,3,4,5,6,7,8 週
星期三8,9,10(15:30~18:20)星期五1,2(8:10~10:00) |
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上課地點 |
普103普103 |
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備註 |
本課程以英語授課。密集課程。英文授課.統一教學.三10實習課.
限本系所學生(含輔系、雙修生) 或 限僑生、國際學生
總人數上限：160人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Building upon the foundation laid in MATH4006-7, which focused on Calculus of functions with a single real variable, Multivariable Calculus (MATH4008-9) delves into the principles and applications of multivariable calculus, particularly in the context of 2- and 3-variable functions. This course serves as a crucial cornerstone for various disciplines in Science and Engineering.
Key topics include
1. Partial Derivatives
2. Continuous and Differentiable Functions in Multivariables
3. Chain Rule and Directional Derivatives:
4. Second Derivative Test and Lagrange Multipliers
5. Double and Triple Integrations
6. Curvilinear Coordinates
In this course, definitions are thoroughly discussed, and key theorems are derived during lectures to foster logical deduction and analytical skills among students. Practical applications of calculus are highlighted to establish a meaningful connection between theoretical concepts and their relevance to various scientific and engineering fields. To enhance students' proficiency in calculus, TA classes are incorporated into the course. Here, students have the opportunity to refine their calculation skills under the guidance of experienced teaching assistants. These sessions aim to reinforce theoretical concepts and provide practical insights into problem-solving techniques. |
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課程目標 |
On successful completion of this module students should be able to:
(1) Compute partial derivatives and understand their geometric meaning
(2) Determine whether a multivariable function is continuous and/or differentiable
(3) Apply the chain rule to compute derivatives of composed functions in multivariables & directional derivatives
(4) Determine local extrema of a given two-variable function
(5) Use Lagrange multiplier to resolve constrained optimization problems
(6) Compute multiple integrations by Fubini's Theorem and/or change of variables
(7) Understand the geometric and physical meanings of multiple integrations |
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課程要求 |
Assumed knowledge :
- MATH4006-7,
- Basic trigonometry, vector geometry,
- Determinants of 2x2 and 3x3 matrices (knowledge in linear algebra will be useful but not necessary) |
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預期每週課前或/與課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
Instructor's lecture notes |
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評量方式
(僅供參考) |
- 本校尚無訂定 A+ 比例上限。
- 本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見學習評量專區 (連結)。
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